This activity is part of a collection of 40 open-ended investigative activities available on the RISPs website. The relevant activity is Risp 17: Six Parabolas.
By varying the coefficients of a quadratic function you can explore the effects of different coefficients. This is a critical step in understanding functions and families of functions. Learners first meet functions as sets of points generated by an independent variable and a calculable function. At this stage the numbers that change are the variables.
As part of the process of shifting towards seeing the function as an object in itself, learners have to focus on the parameters that shape the function. This task triggers exploration of this process, and begins to relate the coefficients to physical characteristics of the parabolae.